The number of rational points of certain quartic diagonal hypersurfaces over finite fields

Zhao, Junyong; Hong, Shaofang; Zhu, Chen

doi:10.3934/math.2020175

Cited by 9 publications

(3 citation statements)

References 14 publications

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“…The special case where all the k i are equal has extensively been studied(see, for instance, Refs. [3][4][5][6][7][8][9][10][11][12][13][14]). This is the example chosen by Weil [10] to illustrate his renowned conjecture on projective varieties over finite fields.…”

Section: Introductionmentioning

confidence: 99%

Note on the Number of Solutions of Cubic Diagonal Equations over Finite Fields

HU,

WANG,

et al. 2023

Wuhan Univ. J. Nat. Sci.

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Let [see formula in PDF] be the finite field, [see formula in PDF], with [see formula in PDF] being a prime and [see formula in PDF] being a positive integer. Let [see formula in PDF] be the multiplicative group of [see formula in PDF], that is [see formula in PDF]. In this paper, by using the Jacobi sums and an analog of Hasse-Davenport theorem, an explicit formula for the number of solutions of cubic diagonal equation [see formula in PDF] over [see formula in PDF] is given, where [see formula in PDF] and [see formula in PDF]. This extends earlier results.

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Section: Introductionmentioning

confidence: 99%

Note on the Number of Solutions of Cubic Diagonal Equations over Finite Fields

HU,

WANG,

et al. 2023

Wuhan Univ. J. Nat. Sci.

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“…Generally, the hydrogen bond comprises a proton donor moiety and a proton acceptor group. And the proton donor and acceptor moieties typically contain the strong electronegative atoms such as O, N, F, and S . The interaction among them could be analogous to that in the covalent bond.…”

Section: Introductionmentioning

confidence: 99%

Unraveling photoexcitation dynamical behavior for bis (salicylidene)‐1,5‐diaminonaphthalene (BSD) system

Wang

Liu

Yang

2019

J of Physical Organic Chem

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In this work, a new excited state intramolecular proton transfer (ESIPT) mechanism of bis (salicylidene)-1,5-diaminonaphthalene (BSD) is proposed based on density functional theory (DFT) and time-dependent DFT methods. Given the intramolecular dual hydrogen bonds of BSD, we explore the excited state hydrogen bonding interactions for BSD and verify that the dual intramolecular hydrogen bonds of BSD molecule should be strengthened in the first excited state. Further, in the analyses about charge distribution upon excitation, we confirm that the charge redistribution around hydrogen bonding moieties plays important roles in enhancing dual hydrogen bonds and in facilitating ESIPT process. To reveal the detailed ESIPT mechanism, we construct the potential energy surfaces (PESs) in both S 0 and S 1 states along with hydrogen bonds. Via comparing potential energy barriers among the stable structures on the S 1 -state PES, we present the excited state intramolecular single proton transfer mechanism for BSD system. Moreover, the phenomenon and properties of fluorescence for BSD in experiment could be explained reasonably based on the ESIPT mechanism presented in this work. KEYWORDS charge redistribution, dual hydrogen bonds, electronic difference density, excited state intramolecular proton transfer, frontier molecular orbital

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“…In addition, the specific photoexcitation process and excited state dynamical behavior about 2 itself is also ambiguous. It is well known that theoretical investigations could provide the detailed excited state process and explain the dynamical mechanism . Therefore, for the better applications about 2 in future, the specific excited state dynamical behaviors about 2 is very important.…”

Section: Introductionmentioning

confidence: 99%

Theoretical elaboration about the excited state dynamical behaviors for a novel fluorescent sensor

Zhang

Jia

et al. 2018

J of Physical Organic Chem

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Using the density functional theory (DFT) and time-dependent density functional theory (TDDFT) methods, we theoretically explore a novel fluorescent sensor molecule (abbreviated as "2") (Sensors Actuat B-Chem. 2018, 263, 585). Because of its symmetry, three stable structures can be located, ie, 2-enol, 2-SPT, and 2-DPT forms in both S 0 and S 1 states. Via comparing the bond lengths and bond angles involved in the hydrogen bonding moieties, we find the dual intramolecular hydrogen bonds should be strengthened in the S 1 state. And based on infrared (IR) vibrational simulations, we further confirm the strengthening dual hydrogen bonds. Upon the photo-excitation process, the charge redistribution via frontier molecular orbitals (MOs) reveals the tendency of excited state intramolecular proton transfer (ESIPT) reaction. In addition, the constructed S 0 -state and S 1 -state potential energy curves demonstrate that the excited state single proton transfer (ESSPT) should be the most supported one from 2-enol to 2-SPT form. In view of the S 1 -state stable 2-SPT and 2-DPT structures as well as the fluorescence peaks of them, we can further confirm the ESSPT mechanism for 2 chemosensor. This work not only clarifies the excited state behaviors of 2 system but also successfully explain the previous experimental phenomenon.

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The number of rational points of certain quartic diagonal hypersurfaces over finite fields

Cited by 9 publications

References 14 publications

Note on the Number of Solutions of Cubic Diagonal Equations over Finite Fields

Note on the Number of Solutions of Cubic Diagonal Equations over Finite Fields

Unraveling photoexcitation dynamical behavior for bis (salicylidene)‐1,5‐diaminonaphthalene (BSD) system

Theoretical elaboration about the excited state dynamical behaviors for a novel fluorescent sensor

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